Compliance Chambers for Marine Vibrators

ABSTRACT

A marine vibrator may include a containment housing, a sound radiating surface, and a compliance chamber. The compliance chamber may include a compliance chamber housing, a non-linear linkage assembly, and a low pressure chamber. The compliance chamber housing may define at least a portion of a compliance chamber internal volume having a compliance chamber internal gas pressure. The low pressure chamber may comprise a low pressure piston and a low pressure chamber housing. The low pressure chamber housing may define at least a portion of a low pressure chamber internal volume having a low pressure chamber internal gas pressure. The low pressure piston may be configured to move in response to a pressure differential across the low pressure piston such that a resonance frequency of the marine vibrator may be changed.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to U.S. Provisional ApplicationNo. 62/064,104, filed on Oct. 15, 2014, the entire disclosure of whichis incorporated herein by reference.

BACKGROUND

Embodiments relate generally to marine vibrators for marine seismicsurveys, and, more particularly, embodiments relate to the use ofcompliance chambers in marine vibrators to compensate for air-springeffects.

Sound sources are generally devices that generate acoustic energy. Oneuse of sound sources is in marine seismic surveying. Sound sources maybe employed to generate acoustic energy that travels downwardly throughwater and into subsurface rock. After interacting with the subsurfacerock, for example, at the boundaries between different subsurfacelayers, some of the acoustic energy may be reflected back toward thewater surface and detected by specialized sensors. The detected energymay be used to infer certain properties of the subsurface rock, such asthe structure, mineral composition and fluid content. These inferencesmay provide information useful in the recovery of hydrocarbons.

Most of the sound sources employed today in marine seismic surveying areof the impulsive type, in which efforts are made to generate as muchenergy as possible during as short a time span as possible. The mostcommonly used of these impulsive-type sources are air guns thattypically utilize a compressed gas to generate a sound wave. Otherexamples of impulsive-type sources include explosives and weight-dropimpulse sources. Marine vibrators are another type of sound source thatcan be used in marine seismic surveying. Types of marine vibrators mayinclude hydraulically powered sources, electro-mechanical vibrators,electrical marine vibrators, or sources employing piezoelectric ormagnetostrictive material. Marine vibrators typically generatevibrations through a range of frequencies in a pattern known as a“sweep” or “chirp.”

A marine vibrator may radiate sound by moving one or more soundradiating surfaces that may be connected to a mechanical actuator.During this motion these surfaces displace a certain volume. Thisdisplaced volume may be the same outside and inside the marine vibrator.Inside the marine vibrator this volume displacement may cause a pressurevariation that in absolute values increases substantially while themarine vibrator is lowered to increasing depths. As the internal gas(e.g., air) in the marine vibrator increases in pressure, the bulkmodulus (or “stiffness”) of the internal gas also rises. Increasing thebulk modulus of the internal gas also increases the air-spring effectwithin the marine vibrator. As used herein, the term “air-spring” isdefined as an enclosed volume of gas that may absorb shock orfluctuations of load due to the ability of the enclosed volume of gas toresist compression. Increasing the stiffness of the gas in the enclosedvolume increases the air-spring effect and thus the ability of theenclosed volume of gas to resist compression. This increase in theair-spring effect of the internal gas tends to be a function of theoperating depth of the source. Further, the stiffness of the acousticcomponents of the marine vibrator and the internal gas are primarydetermining factors in the marine vibrator's resonance frequency.Accordingly, the resonance frequency generated by the marine vibratormay undesirably increase when the marine vibrator is disposed (e.g.,towed) at depth, especially in marine vibrators where the interiorvolume of the marine vibrator may be pressure balanced with the externalhydrostatic pressure. Hence, in marine seismic survey applications itmay be desirable that a resonance frequency can be retainedindependently of the operation depth and/or that the output resonancefrequency can be controlled so as to be below and/or above its nominalresonance frequency.

BRIEF DESCRIPTION OF THE DRAWINGS

These drawings illustrate certain aspects of some of the embodiments ofthe present invention and should not be used to limit or define theinvention.

FIG. 1 illustrates an example embodiment of a flextensional shell-typemarine vibrator comprising a compliance chamber.

FIG. 2 illustrates an example embodiment of a piston plate-type marinevibrator comprising a compliance chamber.

FIG. 3 illustrates an example embodiment of a marine vibrator comprisinga compliance chamber.

FIG. 4 illustrates another example embodiment of a marine vibratorcomprising a compliance chamber.

FIG. 5A illustrates an example embodiment of a compliance chamber.

FIG. 5B illustrates an example embodiment of a compliance chamber.

FIG. 6A illustrates an example embodiment of a marine vibratorcomprising a low pressure piston.

FIG. 6B illustrates an example embodiment of a marine vibratorcomprising a low pressure piston.

FIG. 7 is a graph that plots the work-versus-displacement function of amarine vibrator in accordance with example embodiments.

FIG. 8 is a graph that plots the relationship between the movement of amoveable structure and the movement of a low pressure piston as afunction of displacement.

FIG. 9 is an example embodiment of a marine seismic survey system usinga marine vibrator.

DETAILED DESCRIPTION

It is to be understood that the present disclosure is not limited toparticular devices or methods, which may, of course, vary. It is also tobe understood that the terminology used herein is for the purpose ofdescribing particular embodiments only, and is not intended to belimiting. All numbers and ranges disclosed herein may vary by someamount. Whenever a numerical range with a lower limit and an upper limitis disclosed, any number and any included range falling within the rangeare specifically disclosed. Although individual embodiments arediscussed, the invention covers all combinations of all thoseembodiments. As used herein, the singular forms “a”, “an”, and “the”include singular and plural referents unless the content clearlydictates otherwise. Furthermore, the word “may” is used throughout thisapplication in a permissive sense (i.e., having the potential to, beingable to), not in a mandatory sense (i.e., must). The term “include,” andderivations thereof, mean “including, but not limited to.” The term“coupled” means directly or indirectly connected. If there is anyconflict in the usages of a word or term in this specification and oneor more patent or other documents that may be incorporated herein byreference, the definitions that are consistent with this specificationshould be adopted for the purposes of understanding the invention.

Embodiments relate generally to marine vibrators for marine seismicsurveys, and, more particularly, embodiments relate to the use ofcompliance chambers in marine vibrators, which may compensate forair-spring effects. As discussed in more detail below, the compliancechamber may shift the resonance frequency of the marine vibrator lowerand may also increase the sound output at lower frequencies.Advantageously, the marine vibrators may display a low resonancefrequency in the seismic frequency range of interest. In particularembodiments, the marine vibrators may display a first resonancefrequency within the seismic frequency range of about 1 Hz to about 10Hz when submerged in water at a depth of from about 0 meters to about300 meters.

Marine vibrators may be used in marine seismic surveying to generateacoustic energy that may travel downwardly through water and downwardlyinto the subsurface rock. Embodiments of the marine vibrators mayinclude flextensional shell-type marine vibrators, piston plate marinevibrators, hydraulically powered vibrators, electro-mechanicalvibrators, electrical marine vibrators, and vibrators employingelectrostrictive (e.g., piezoelectric) or magnetostrictive material. Itis to be noted that unless specifically excluded, any disclosureregarding compliance chambers may be embodied by any of the embodimentsof the type of marine vibrators discussed herein and that no embodimentof a compliance chamber is to be restricted to a specific type of marinevibrator.

Flextensional shell-type marine vibrators may include actuators andtransducers and may act as mechanical transformers by transforming andamplifying the displacement to meet the demands of differentapplications. Flextensional shell-type marine vibrators are generallymarine vibrators having an outer shell that moves back and forth andflexes to generate acoustic energy. An example embodiment offlextensional shell-type marine vibrator 5 is illustrated in FIG. 1. Inthe example embodiment, the flextensional shell-type marine vibrator 5employs one or more compliance chambers 10, for example, to compensatefor pressure changes of the internal gas pressure. The flextensionalshell-type marine vibrator 5 of FIG. 1 is shown in partialcross-section. As illustrated, the flextensional shell-type marinevibrator 5 may be mounted within a frame 15. A bracket 20 may be mountedto the top of the frame 15. The bracket 20 may be used for deploying theflextensional shell-type marine vibrator 5 in a body of water. Theflextensional shell-type marine vibrator 5 may comprise at least onesound radiating surface 21 as illustrated by outer shell 25. Asillustrated, the compliance chambers 10 may be disposed within the outershell 25. Alternatively, compliance chambers 10 may be disposed on theexterior of outer shell 25. While FIG. 1 illustrates two compliancechambers 10 disposed within the outer shell 25, it should be understoodthat the invention is applicable to the use of any number of compliancechambers 10 with a flextensional shell-type marine vibrator 5. By way ofexample, embodiments may include the use of one, two, three, four, ormore compliance chambers 10 for the flextensional shell-type marinevibrator 5. In the illustrated embodiment, the outer shell 25 may beelliptical in shape or other suitable shape, including convex, concave,flat, or combinations thereof While not illustrated, the outer shell 25may be formed, for example, by two shell side portions that may bemirror images of one another.

Piston plate-type marine vibrators are generally marine vibrators havinga piston plate that moves back and forth to generate acoustic energy.FIG. 2 is an example embodiment of a piston plate-type marine vibrator,illustrated as piston plate-type marine vibrator 30. As illustrated,piston plate-type marine vibrator 30 may comprise at least one soundradiating surface 21 and compliance chambers 10. The at least one soundradiating surface 21 is illustrated on FIG. 2 by piston plates 35. Inthe illustrated embodiment, compliance chambers 10 are disposed on theexterior of containment housing 135 of the piston plate-type marinevibrator 30. In alternative embodiments, compliance chambers 10 may bedisposed on the interior of containment housing 135 of piston plate-typemarine vibrator 30. While FIG. 2 illustrates two compliance chambers 10disposed on the exterior of containment housing 135 of piston plate-type marine vibrator 30, it should be understood that the invention isapplicable to the use of any number of compliance chambers 10 with apiston plate-type marine vibrator 30. By way of example, embodiments mayinclude the use of one, two, three, four, or more compliance chambers 10for the piston plate-type marine vibrator 30. Piston plate-type marinevibrator 30 may include brackets 20, which may be separately mounted onopposing sides of piston plate-type marine vibrator 30, or may bemounted on adjacent sides. Alternatively, only one bracket 20 may beused. Brackets 20 may be used for hoisting piston plate-type marinevibrator 30, for example when a deploying piston plate-type marinevibrator 30 in the water. By way of example, brackets 20 may facilitateattachment of piston plate marine vibrator 30 to tow lines, a surveyvessel (e.g., survey vessel 155 on FIG. 8), or other suitable device ormechanism used in conjunction with disposing or towing piston plate-typemarine vibrator 30 through a body of water.

Any of the marine vibrators (e.g., flextensional shell-type marinevibrator 5 on FIG. 1 and piston plate-type marine vibrator 30 on FIG. 2)discussed herein may have an internal gas pressure. By way of example,the marine vibrator may define an internal volume in which a gas may bedisposed. The internal volume of a marine vibrator will be referred toherein as the “marine vibrator internal volume.” In some embodiments,the marine vibrators may have a pressure compensation system. Thepressure compensation system may be used, for example, to equalize theinternal gas pressure of the marine vibrator with the external pressure.The internal gas pressure of the marine vibrator will be referred toherein as the “marine vibrator internal gas pressure.” Pressurecompensation may be used, for example, where a marine vibrator needs tobe disposed (e.g., towed) at depth to achieve a given level of output.As the depth of a marine vibrator increases, the marine vibratorinternal gas pressure may be increased to equalize pressure with theincreasing external pressure. For example, a gas (e.g., air) or liquid(e.g., water) may be introduced into the marine vibrator to increase themarine vibrator internal gas pressure to approach and/or equalizepressure with the increasing external pressure. In some embodiments, theintroduced gas or liquid may undergo a phase transition due to changingconditions within the marine vibrator (e.g., a change in pressure,temperature, etc.). Shifting the phase of matter may increase the marinevibrator internal gas pressure to approach and/or equalize theincreasing external pressure.

Without being limited by theory, increasing the marine vibrator internalgas pressure may create an air-spring effect that may undesirably impactthe resonance frequency of the marine vibrators. In particular, theresonance frequency may increase as the marine vibrator internal gaspressure increases. Those of ordinary skill in the art, with the benefitof this disclosure, should appreciate that an increase in the marinevibrator internal gas pressure may also result in an increase of thebulk modulus or air-spring effect of the gas (e.g., air) in the marinevibrator. Among other things, the resonance frequency of the marinevibrator may be based on the combination of the gas spring of the gas inthe marine vibrator and the spring constant of any spring component ofthe marine vibrator (e.g., mechanical springs, nonmechanical springs,linear springs, non-linear springs, etc). Thus, increasing the bulkmodulus or gas spring effect of the internal gas of a marine vibratormay also result in an increase in the resonance frequency. As such, theresonance frequency of a marine vibrator disposed at depth mayundesirably increase when the marine vibrator internal gas pressure iscompensated by equalization with the external pressure (e.g., by using apressure compensation system).

To compensate for changes in the marine vibrator internal gas pressure,compliance chamber 10 may be employed. The compliance chamber 10 maycontain a gas (e.g., air). The internal volume of compliance chamber 10will be referred to herein as the “compliance chamber internal volume.”The internal gas pressure of compliance chamber 10 will be referred toherein as the “compliance chamber internal gas pressure.”

In some embodiments, compliance chamber 10 may comprise a sealed volumewith a compliance chamber internal gas pressure of less than 1atmosphere when at the water surface (less than about 1 meter depth).Alternatively, the compliance chamber internal gas pressure may be equalto or greater than atmospheric pressure when at the water surface.Further alternatively, the compliance chamber internal gas pressure maybe equal to or lesser than atmospheric pressure when at the watersurface. In present embodiments, when the marine vibrators are atoperational depth, the compliance chamber internal gas pressure may beless than the marine vibrator internal gas pressure. In someembodiments, the marine vibrators may be operated, for example, at adepth of from about 1 meter to about 300 meters and, more particularly,from about 1 meter to about 100 meters.

In some embodiments, as illustrated in FIG. 3, a compliance chamber 10may comprise at least one piston attached by an elastic component (e.g.,a bellow (not shown) connected to a wall of the compliance chamber 10).In various embodiments, the pressurized gas within the marine vibratorinternal volume can act on the outside of the compliance chamber piston60, and a compressed gas within the compliance chamber internal volumecan act from inside the compliance chamber 10 against the other side ofthe same piston. An example embodiment if this type of compliancechamber 10 is generally illustrated by FIG. 3. As illustrated, marinevibrator internal volume 40 is disposed within marine vibrator 45. Asillustrated in FIG. 3, marine vibrator 45 comprises a piston plate-typemarine vibrator 30. However, in alternative embodiments, marine vibrator45 may be any type of marine vibrator including flextensional shell-typemarine vibrator 5 as illustrated in FIG. 1. In the illustratedembodiment, marine vibrator internal volume 40 may contain a gas, suchas air, to provide a marine vibrator internal gas pressure. Compliancechamber 10 may be in contact with marine vibrator internal volume 40.Compliance chamber 10 may be connected to containment housing 135 ofmarine vibrator 45 in any suitable manner. Compliance chamber 10 mayhave a compliance chamber internal volume 50, which may provide acompliance chamber internal gas pressure. In embodiments, compliancechamber internal volume 50 may contain a gas (e.g., air). In accordancewith present embodiments, compliance chamber internal volume 50 may besealed so as to not result in the chamber internal gas being in contactwith any marine vibrator internal gas present in marine vibratorinternal volume 40. In other embodiments, the compliance chamberinternal gas pressure may be equal to or higher than the marine vibratorinternal gas pressure.

As illustrated by FIG. 3, compliance chamber 10 may comprise acompliance chamber housing 55, a moveable structure 56, and an optionalspring element 65. In some embodiments, compliance chamber internalvolume 50 may be defined by compliance chamber housing 55 and a moveablestructure 56 which comprises compliance chamber piston 60. Compliancechamber housing 55 may be made of any such suitable materials,including, without limitation, metals and plastics. Compliance chamberpiston 60 may be slidable in compliance chamber housing 55 such that,when driven into or out of compliance chamber housing 55, the compliancechamber internal volume 50 may be changed. Compliance chamber piston 60may be designed with sufficient displacement in compliance chamberhousing 55 to compensate for a change in marine vibrator internal gaspressure, for example, due to a change in depth and/or any change inmarine vibrator internal volume 40 due to the operation of a marinevibrator 45. The compliance chamber piston 60 may be sealed incompliance chamber housing 55, for example, with an O-ring, rubber seal,piston rings, bellows, etc. Compliance chamber piston 60 may be a disk,cylindrical element, or any configuration suitable to effect a desiredcompliance chamber internal volume change in compliance chamber housing55. For example, compliance chamber piston 60 may have a differentconfiguration, including square, rectangular, or oblong, among others.In some embodiments, compliance chamber piston 60 may be loaded incompliance chamber housing 55 with spring element 65.

Spring element 65 may be tuned to form a resonant system together withthe mass of the compliance chamber piston 60, enabling a resonance closeto the desired resonance of the marine vibrator. In optionalembodiments, spring element 65 may be a linear spring. As illustrated inFIG. 3, in optional embodiments, spring element 65 may be disposedwithin compliance chamber internal volume 50 and attached to compliancechamber piston 60. Spring element 65 may be any spring suitable forcreating a resonant system formed by the compliance chamber piston 60mass, the mass of its load, the air spring, and said spring element 65.Spring element 65 may be used to obtain a marine vibrator 45 resonancefrequency that is almost independent of depth. Spring element 65 mayalso have a biasing effect, enabling the compliance chamber internalpressure to differ from marine vibrator internal pressure. By way ofexample, spring element 65 may be a compression spring, a torsionspring, and the like.

With continued reference to FIG. 3, compliance chamber 10 may furthercomprise a low pressure chamber 70 and a non-linear linkage assembly 85.Low pressure chamber 70 may comprise a low pressure piston 75 and a lowpressure chamber housing 76 which define a low pressure chamber internalvolume 80 having a low pressure chamber internal gas pressure. Lowpressure chamber internal volume 80 comprises a low pressure relative tothe compliance chamber internal gas pressure and the marine vibratorinternal gas pressure. “Low pressure” when used in the context of lowpressure chamber 70 and low pressure piston 75 is defined as a pressurethat is a maximum of 50% of the pressure on the high pressure side ofthe low pressure piston. Specifically, the low pressure chamber internalvolume will comprise a pressure that does not exceed 50% of the pressureon the other side of the low pressure piston or put in another way, thelow pressure chamber 70 will comprise an internal pressure that does notexceed 50% of the pressure external to the low pressure chamber 70. Lowpressure piston 75 may be connected to moveable structure 56, which asillustrated in FIG, 3 is compliance chamber piston 60. The connectionbetween low pressure piston 75 and compliance chamber piston 60 may beany such connection suitable for affixing one to the other such that themovement of one may influence the movement of the other.

As illustrated by FIG. 3, low pressure piston 75 may be connected tomoveable structure 56 by a non-linear linkage assembly 85. Non-linearlinkage assembly 85 may be any such linkage assembly that links lowpressure piston 75 and moveable structure 56 in a non-linearrelationship. In this specific embodiment, non-linear linkage assembly85 comprises low pressure chamber belt 91, moveable structure belt 90,and camshaft 95. The low pressure chamber belt 91 may be coupled tocamshaft 95 and low pressure piston 75 in any manner. Moveable structurebelt 90 may be coupled to camshaft 95 and moveable structure 56 (e.g.,compliance chamber piston 60) in any manner. Low pressure chamber belt91 and moveable structure belt 90 may be made of any materialssufficient for the applications described herein. Examples of materialsmay include, but should not be limited to plastics such as natural andsynthetic rubbers, steel, KEVLAR®, and the like. KEVLAR® is a registeredtrademark of the E. I. du Pont de Nemours and Company, of Wilmington,Del. The materials may be elastic or nonelastic. The stiffness of thematerial may affect the force applied and the material should beselected accordingly. In alternative embodiments, low pressure chamberbelt 91 and moveable structure belt 90 may be substituted for a pistonrod (not shown). Camshaft 95 may be any camshaft suitable fortranslating the displacement of low pressure piston 75 as low pressurepiston 75 moves inward into low pressure chamber internal volume 80 to aforce necessary to assist in pulling moveable structure 56 inward intocompliance chamber internal volume 50. Although FIG. 3 specificallyillustrates a camshaft 95, it is to be understood that any structure ormechanical linkage capable of transferring the driving performed by lowpressure piston 75 to a force sufficient to move moveable structure 56may be used.

Operation of compliance chamber 10, as shown in FIG. 3, will now bedescribed in accordance with the example embodiment. Compliance chamber10 may operate due to a change in the pressure differential acrossmoveable structure 56 (illustrated by compliance chamber piston 60 inFIG. 3) between the marine vibrator internal volume 40 and thecompliance chamber internal volume 50. By way of example, the change inthe pressure differential may be caused by an increase in the marinevibrator internal gas pressure due to increased depth and/or theacoustic operation of marine vibrator 45. For example, sound radiatingsurface 21 comprising piston plate 35 may move back and forth (asillustrated by arrows 100) to generate acoustic vibrations. In theillustrated embodiment, movement of piston plate 35 may be induced by anactuator 105. The resulting force due to the pressure differentialbetween the marine vibrator internal volume 40 and the compliancechamber internal volume 50 may result in compliance chamber piston 60being displaced into compliance chamber internal volume 50. Such adisplacement may increase the pressure within compliance chamberinternal volume 50. This pressure increase may result in a counteractingforce acting on compliance chamber piston 60 from within the compliancechamber 10. The counteracting force results from the compression of thegas within compliance chamber 10. This compressed gas force will bereferred to herein as the chamber gas spring 110 (e.g., an air spring).The counteracting force may act in tandem with optional spring element65 if spring element 65 is provided. The chamber gas spring 110 and, ifpresent, optional spring element 65, may have a positive spring rate (ameasurement of amount of force required to deflect a spring a specifieddistance; a lower spring rate corresponds with a softer spring). Theforce exerted by the chamber gas spring 110 and, if present, optionalspring element 65, may increase as the compliance chamber piston 60 ismoved further into compliance chamber 10, thus displacing more of thecompliance chamber internal volume 50. The force exerted on thecompliance chamber piston 60 may be approximately proportional to themarine vibrator internal gas pressure in the marine vibrator 45, sincethe compliance chamber 10 may be operated with a pressure slightlyhigher than the marine vibrator internal gas pressure in the marinevibrator 45.

In order to maintain the pressure in marine vibrator internal volume 40nearly constant regardless of the marine vibrator internal volumedisplacement, and therefore keep the marine vibrator internal gaspressure independent of the compliance chamber piston 60 position, aforce balance on the moveable structure 56 may be used to assist inpulling the moveable structure 56 inward. Without such force, moveablestructure 56 may get stiffer as it moved inward. A correction forcedescribed herein as force A and identified by reference marker 115 maybe applied to the compliance chamber piston 60 (i.e. moveable structure56) via non-linear linkage assembly 85 (or any similar mechanism)connected to low pressure piston 75. Force A 115 may increase as thecompliance chamber piston 60 displaces more of compliance chamberinternal volume 50. The force-versus-displacement function of force A115 may correspond to a spring with negative spring rate. Said force A115 may, for any given displacement X of compliance chamber piston 60(i.e. moveable structure 56), cancel the force increase caused by thecompression of the chamber gas spring 110. As a result, the marinevibrator internal gas pressure may remain almost constant independent ofpiston plate 35 displacement. Thus, the variation in effective stiffnessdue to depth variations and therefore the marine vibrator internal gaspressure may be reduced. The resonance frequency may be directly relatedto the effective spring stiffness. Stiffness effects (i.e., theair-spring effect) on the marine vibrator 45 resonance frequency may bereduced.

Force B 120 is a force generated by low pressure piston 75 as lowpressure piston 75 moves into low pressure chamber 70, driven by thepressure of chamber gas spring 110. Said movement decreases the volumeof low pressure chamber internal volume 80 and at the same timeincreases the volume of compliance chamber internal volume 50. Asdesired, the gear-versus-displacement function of the non-linear linkageassembly 85 may be used to ensure that the force B 120 generated bydisplacement of low pressure piston 75 is converted to provide a desiredamount of corrective force (i.e. force A 115) using a non-linear gear.For example, in this embodiment, camshaft 95 may be adjusted as desiredto suit the application. The low pressure piston generated force ofForce B 120, which is the force on the low pressure chamber belt 91,will increase as the pressure inside compliance chamber 10 increases.When the operation of marine vibrator 45 is initiated, low pressurepiston 75 may move slowly as compliance chamber piston 60 moves inwardinto compliance chamber internal volume 50, but may accelerate thefurther compliance chamber piston 60 moves inward into compliancechamber internal volume 50. This is due to the non-linear relationshipbetween compliance chamber piston 60 and low pressure piston 75. In thisembodiment, the mechanical coupling between compliance chamber piston 60and low pressure piston 75 is not proportional: the two move in anon-linear relationship due to the non-linear linkage assembly 85 whichlinks the displacement of low pressure piston 75 with the displacementof compliance chamber piston 60. The volume displacement of thecompliance chamber piston 60 may be approximately equal to the volumedisplacement of the sound radiating surface 21, and the relationship inmovement between the sound radiating surface 21, and the low pressurepiston 75 would, therefore, be non-linear. As illustrated, the use ofthe low pressure piston 75 as a force generator (i.e. it generates lowpressure piston force, Force B 120) placed inside the compliance chamberinternal volume 50 may result in Force B 120 changing when pressure ischanging in the compliance chamber internal volume 50 due to thecompression of the chamber gas spring 110. As such, a force generated onmoveable structure 56 (e.g., sound radiating surface 21) by the marinevibrator internal gas pressure and/or the chamber gas spring 110 may bemitigated. During a compression cycle, the temperature of any gas in thecompliance chamber internal volume 50 may increase due to the rapiditywith which the compliance chamber internal volume 50 may be altered bythe movement of compliance chamber piston 60. For a compression stroke,the pressure increase can be close to an adiabatic process, for example,if the compliance chamber piston 60 is left in its most displaced state,the system can initially be in balance, if a particular gear-ratio hasbeen selected to allow for this state. As such, the compliance chamberinternal gas pressure may decrease when the gas comprising the chambergas spring 110 cools. Thus, the low pressure piston generated force ofForce B 120 may decrease as the gas within the compliance chamberinternal volume 50 cools, maintaining a force balance on compliancechamber piston 60.

The example illustrated by FIG. 3 may work with an internal gas, such asair, at a pressure close to the hydrostatic pressure surrounding themarine vibrator 45. When the marine vibrator 45 is exposed to increasingpressure, due to increasing water depth, the correction force of force A115 may increase proportionally. The pressure in the compliance chamber10 may be kept at a pressure close to the outside water pressure at thedepth of operation. For example, when the depth is increased, so is thepressure in the compliance chamber 10. As such, a larger force A 115 maybe needed at larger depths in order to maintain a force balance oncompliance chamber piston 60 when the moveable structure 56 is pushedinwards compressing the compliance chamber internal gas and increasingthe chamber gas spring 110. The low pressure piston 75 may generateproportionally more force as pressure is increased in the compliancechamber 10, assuming that the pressure in low pressure chamber 70 is low(i.e., approaching a vacuum). Thus, this functionality allows foroperation of marine vibrator 45 at different depths, and as such, marinevibrator 45 does not need to be maintained at a constant depth in orderto function. For example, in an embodiment, a marine vibrator operatedat a first depth and having a first resonance frequency may then bemoved and operated at a second depth greater than the first depth andhave a second resonance frequency. In this example, the marine vibratorinternal gas pressure may be allowed to act on the low pressure piston75 such that the first resonance frequency differs from the secondresonance frequency by no more than 25%. For example, the firstresonance frequency may differ from the second resonance frequency by nomore than 20%, by no more than 15%, by no more than 10%, or by no morethan 5%.

In embodiments, the marine vibrator 45 may be towed through a body ofwater over a subterranean formation. A seismic signal may be generatedfrom the sound radiating surface 21 of the marine vibrator 45 as it isactuated. The seismic signal may comprise a specific resonancefrequency. The resonance frequency generated will have a peak power at aspecific resonance frequency. The power (e.g., Watt, decibel, etc.) ofthe seismic signal will determine the degree to which it is able topenetrate the subterranean formation, and thus, the modified seismicsignal detected by the marine vibrator 45 is influenced by the power ofthe seismic signal and thus the resonance frequency of the seismicsignal. In embodiments, the resonance frequency and thus the power ofthe seismic signal may be adjusted by the adjustment of the marinevibrator internal gas pressure. As described in FIG. 3, the adjustmentof the marine vibrator internal gas pressure may be accomplished byallowing the marine vibrator internal gas pressure to act on the lowpressure piston 75 of the low pressure chamber 70. Thus, as the depth ofthe marine vibrator 45 is altered, the low pressure chamber 70 allowsfor control of the power output of the seismic signal independent ofdepth. In embodiments, this may allow the marine vibrator 45 to attain apeak power output at two different depths, wherein the peak power outputis a power associated with a resonance frequency in the seismicfrequency range of interest (i.e. about 1 Hz to about 10 Hz).

FIG. 4 illustrates an example marine vibrator 45 and compliance chamber10 that is similar to the example of FIG. 3 except that the moveablestructure 56 illustrated in FIG. 4 comprises piston plate 35 and notcompliance chamber piston 60, which is not included in this specificexample. As illustrated marine vibrator 45 and compliance chamber 10 nowshare an internal volume, noted as combined internal volume 125. Sincethere is no partition between the marine vibrator 45 and compliancechamber 10, there is only one internal gas pressure and thus one gasspring (e.g., an air spring), noted as combined gas spring 130. Asillustrated, non-linear linkage assembly 85 couples piston plate 35 tolow pressure piston 75 via low pressure chamber belt 91, moveablestructure belt 90, and camshaft 95. An optional spring element 65 mayalso be affixed to piston plate 35. In FIG. 4, combined gas spring 130acts on piston plate 35 as piston plate 35 is displaced inward due tomovement of the actuator 105 or external pressure. In order to keep theforce of the actuator 105 acting on the piston plate 35 independent ofthe piston plate 35 position, force A 115 may be applied to the pistonplate 35 via moveable structure belt 90, said force A 115 being drivenby the displacement of camshaft 95 and low pressure piston 75 as lowpressure piston 75 moves inward into low pressure chamber internalvolume 80 and thus pulls low pressure chamber belt 91. This mechanism isanalogous to that described above in FIG. 3. Thus, force A 115 mayincrease as the piston plate 35 displaces more of the combined internalvolume 125. The force-versus-displacement function of force A 115 maycorrespond to a spring with negative spring rate. For example, adisplacement X of the sound radiating surface 21 may cancel the forceincrease caused by the compression of the combined gas spring 130. As aresult, the air-spring effect may be reduced, resulting in lessvariation on the marine vibrator 45 resonance frequency as a function ofdepth/pressure.

Force B 120 is a force generated by low pressure piston 75 as lowpressure piston 75 moves into low pressure chamber 70, displacing anincreasing volume of low pressure chamber internal volume 80. The lowpressure piston 75 is driven mainly by the pressure inside the combinedinternal volume 125. As desired, the gear-versus-displacement functionof the non-linear linkage assembly 85 may be used to ensure that theforce B 120 generated by displacement of low pressure piston 75 and thecamshaft 95 is converted to provide a desired amount of force A 115. Forexample, in this embodiment, camshaft 95 may be adjusted as desired tosuit the application. Force B 120, which is the force on the lowpressure chamber belt 91, will increase as the combined gas spring 130increases. When the operation of marine vibrator 45 is initiated, lowpressure piston 75 may move slowly as sound radiating surface 21 movesinward into combined internal volume 125, but may accelerate the furthersound radiating surface 21 moves inward into combined internal volume125. This is due to the non-linear relationship between sound radiatingsurface 21 and low pressure piston 75. In this embodiment, soundradiating surface 21 and low pressure piston 75 are physically coupledtogether, and the two exist in a non-linear relationship due to thenon-linear linkage assembly 85, which links the displacement of lowpressure piston 75 with the displacement of sound radiating surface 21.As illustrated, the use of the low pressure piston 75 as a forcegenerator placed inside the combined internal volume 125 may result inforce B 120 changing when pressure is changing in the combined internalvolume 125 due to the compression of the combined gas spring 130. Assuch, a force generated on moveable structure 56 (e.g., sound radiatingsurface 21) by the marine vibrator internal gas pressure and/or thecompliance chamber internal gas pressure may be mitigated. During acompression cycle, the temperature of any gas in the combined internalvolume 125 may increase due to the rapidity with which the combinedinternal volume 125 may be altered by the movement of moveable structure56 (i.e., sound radiating surface 21, and in this specific embodiment,piston plate 35). For a compression stroke, the pressure increase can beclose to an adiabatic process, for example, if the moveable structure 56is left in its most displaced state, the system can initially be inbalance, if a particular gear-ratio has been selected to allow for thisstate. As such, the chamber internal pressure may decrease when the gascomprising the combined gas spring 130 cools. Thus, force B 120 maydecrease as the gas within the combined internal volume 125 cools,maintaining a force balance on piston plate 35.

FIGS. 5A and 5B illustrate an example option for an arrangement of thecomponents within a compliance chamber 10. FIGS. 5A and 5B alsoillustrate the action of a non-linear linkage assembly 85 by furtherillustrating the movement of a moveable structure belt 90, camshaft 95,and low pressure chamber 91 belt within this example arrangement. Thecompliance chamber 10 of FIGS. 5A and 5B may be analogous in function tothe compliance chamber 10 of FIG. 3, but with the structural componentsarranged in a different orientation. FIG. 5A illustrates moveablestructure 56, illustrated in FIG. 5A as comprising compliance chamberpiston 60 in an initial starting position where compliance chamberpiston 60 is displacing a minimum amount of marine vibrator internalvolume 40 (not shown). In an analogous fashion to FIGS. 3 and 4, it isthe actuator (not shown) moving the piston plate, or other soundradiating surface (not shown), that moves the gas in the marine vibratorinternal volume (not shown) and causes the compliance chamber piston 60to move inward as illustrated by FIG. 5B which compresses the chambergas spring 110. As the marine vibrator internal gas pressure increases,low pressure piston 75 may displace at least a portion of low pressurechamber internal volume 80, as illustrated in FIG. 5B. As low pressurepiston 75 moves, moveable structure belt 90, low pressure chamber belt91, and camshaft 95, which couple the low pressure piston 75 to themoveable structure 56 in a non-linear relationship, operate to exert aforce on moveable structure 56. As described above, such movement mayprovide a counteracting force to the increase of the chamber gas spring110 due to compression of compliance chamber internal volume 50 bymovement of compliance chamber piston 60. As such, the marine vibratorinternal gas pressure may be maintained almost independent of thecompliance chamber piston 60 position, and the marine vibrator internalgas pressure is kept near constant. Thus, the internal marine vibratorinternal gas pressure may remain near constant independent of depth, andstiffness effects (i.e., the air-spring effect) on the marine vibrator45 resonance frequency may be reduced.

FIGS. 6A and 6B illustrate an additional embodiment of a pistonplate-type marine vibrator 30 as shown in FIGS. 3 and 4, but using adifferent non-linear linkage assembly 85. The moveable structures arecoupled to low pressure piston 75 via the non-linear linkage assembly85, and a similar effect is produced by the coupling as was described inFIGS. 3 and 4. However, in this specific embodiment, the non-linearlinkage assembly 85 does not comprise moveable structure belt 90, lowpressure chamber belt 91, and camshaft 95. As a substitute for thesecomponents, non-linear linkage assembly 85 comprises ball bearings 92and ribs 93. Ribs 93 may be a component of moveable structure 56, or maybe attached to moveable structure 56. As the pressure within thecombined volume 125 increases, low pressure piston 75 moves inward intolow pressure chamber 70, displacing at least a portion of low pressurechamber internal volume 80, generating force A 115. Ball bearings 92interact with moveable structure ribs 93 to pull moveable structure 56inwards. The slope of moveable structure ribs 93 may be altered toachieve the desired gear-versus-displacement function in an analogousfashion to the alteration of the camshaft 95 described above in FIGS.3-5B. FIG. 6A depicts the moveable structure 56 moved completelyinwards. FIG. 6B depicts the moveable structure 56 extended completelyoutwards. As shown in FIG. 6B the slope of the exterior surface 94 ofthe moveable structure ribs 93 is approaching infinity at the base ofthe moveable structure ribs 93 where the exterior surface 94 contactsthe ball bearings 92. Ball bearings 92, rather than rolling on themoveable structure ribs 93, instead merely pull against the moveablestructure ribs 93 as low pressure piston 75 moves inward into lowpressure chamber internal volume 80, without generating an inwardspulling force on moveable structure 56. However, should a sufficientamount of force against the exterior of moveable structure 56 beapplied, for example by an actuator (not shown for simplicity), moveablestructure 56 may move downward, and consequently movable structure ribs93 may also move downward into the combined internal volume 125. Asmovable structure ribs 93 move downward into combined internal volume125, the slope of movable structure ribs 93 no longer approachesinfinity, and the exterior surface 94 may comprise a slope with whichball bearings 92 may interact. Ball bearings 92 may then roll onexterior surface 94 of moveable structure ribs 93, pushing moveablestructure 56 downwards into the combined internal volume 125 as lowpressure piston 75 moves into low pressure chamber 70, displacing atleast a portion of low pressure chamber internal volume 80. Moveablestructure 56 may continue to move inwards, and may ultimately reach theposition shown in FIG. 6A. Thus, a force balance may be maintained onmoveable structure 56, and the marine vibrator internal gas pressure mayremain constant independent of depth, and stiffness effects (i.e., theair-spring effect) on the marine vibrator 45 resonance frequency may bereduced.

With reference to FIGS. 3-6B, in some examples, for the compliancechamber 10 to mitigate stiffness effects within marine vibrator 45, thecompressed gas spring elements (either chamber gas spring 110 orcombined gas spring 130) and also spring element 65, if present, and theapplied correction force, force A 115 may be stiff enough such that thesystem may be balanced with the current water and/or gas pressure atactual operating depths and also be compliant enough to follow thedisplaced volume variations of the sound radiating surfaces 21 of themarine vibrator 45. When the sound generating surfaces 21 of the marinevibrator 45 displace a volume, the compliance chamber 10 describedherein may function such that the compliance chamber 10 follows thechanges of the displaced volume and the marine vibrator internal volume40 and the marine vibrator internal gas pressure are held nearlyconstant.

The correction force, force A 115, in FIGS. 3-6B, may be proportional tothe pressure difference across the moveable structure 56. In someexamples of the present disclosure, if the pressure is approximatelyequal on both sides of moveable structure 56, no correction force, forceA 115, may be necessary. As previously noted, the resonance frequency atoperational depth may be increased since the mass is forming a tunedsystem together with a stiff spring. By increasing the pressure in thelow pressure chamber internal volume 80, the differential pressureacross the low pressure piston 75 may decrease. This differentialpressure decrease may result in an increase of the effective springstiffness acting on moveable structure 56 in FIGS. 3-6B. Thus, themechanical resonance frequency of a marine vibrator 45 may, at a givendepth, be changed by changing the pressure differential across lowpressure piston 75. Therefore, when a marine vibrator 45 operates at alow frequency, the wavelength may be significantly larger than thedimensions of the vibrator, the pressure and velocity may not be inphase on the sound radiating surface 21, and the water load may bereactive. As such, the transducer displacement may be maximized in orderto generate sufficient acoustic energy. Transmission of, for example, achirp signal may be done at resonance throughout the transmission pulseby changing the pressure differential across low pressure piston 75 astransmission progresses.

The non-linear linkage between the low pressure piston 75 in FIGS. 3-6Band the movable structures 56 may be realized in many different waysusing any combination of rollers, wheels, bearing, curved surfaces,belts, metal bands, wires, ropes, etc. For example, rollers fitted onthe movable structure 56 may roll directly onto a curved camshaftsurface, rather than a camshaft 95 and a movable structure 56 beinginterconnected (e.g., with belts).

In accordance with example embodiments, external energy sources may notbe required for operation of the compliance chamber 10. Instead,embodiments of the compliance chamber 10 may operate due to a change inpressure differential (e.g., across a moveable structure 56, lowpressure piston 75, etc.) between cavities, chambers, bodies of water,etc. with different internal pressures.

With reference to FIGS. 1-6B, compliance chamber 10 may be disposed on aflextensional shell-type marine vibrator 5 as shown in FIG. 1, a pistonplate-type marine vibrator 30 as shown in FIGS. 2, 3, 4, 6A, and 6B oron any other type of marine vibrator 45 by being coupled to containmenthousing 135 of marine vibrator 45. Compliance chamber 10 may be incontact with marine vibrator internal volume 40 through an opening,port, window, or the like in containment housing 135. Containmenthousing 135 may at least partially define marine vibrator internalvolume 40. However, contact between marine vibrator 45 and compliancechamber 10 does not imply that any liquid or gas residing in eithermarine vibrator 45 or compliance chamber 10 is able to pass into theother, as illustrated by FIGS. 3, 5A, and 5B. The marine vibratorinternal gas and the chamber internal gas may not be mixed, and as suchare not exposed to one another. Similarly, the marine vibrator internalvolume 40 and compliance chamber internal volume 50 may be not mixed,and as such are not exposed to one another. In alternative embodiments,however, the volumes and internal gas or gases of the marine vibrator 45and the compliance chamber 10 may be in contact with each and also maybe mixed, as illustrated in FIGS. 4, 6A, and 6B. In all embodiments ofthe compliance chamber 10, changes in the marine vibrator internal gaspressure may effect a change in the compliance chamber internal gaspressure, and vice versa. Compliance chamber 10 may be disposed on theexterior of any part of containment housing 135. In alternativeembodiments, compliance chamber 10 may be disposed on the interior ofcontainment housing 135 of any type of marine vibrator 45. Compliancechamber 10 may be coupled to containment housing 135 using anysufficient means, for example, a threaded connection. Compliance chamber10 may be in contact with marine vibrator internal volume 40 through ahole, opening, port, or the like in containment housing 135.

In some embodiments, marine vibrator 45 may produce at least oneresonance frequency between about 1 Hz to about 200 Hz when submerged inwater at a depth of from about 0 meters to about 300 meters. Inalternative embodiments, marine vibrator 45 may display at least oneresonance frequency between about 0.1 Hz and about 100 Hz,alternatively, between about 0.1 Hz and about 10 Hz, and alternatively,between about 0.1 Hz and about 5 Hz when submerged in water at a depthof from about 0 meters to about 300 meters. Marine vibrator 45 may bereferred to as a very low frequency source where it has at least oneresonance frequency of about 10 Hz or lower.

FIG. 7 illustrates a graph plotted as a function of vibratordisplacement (x-axis) in accordance with the embodiments of the presentdisclosure. The work (y-axis) needed to compress a given volume of gasin a gas spring (e.g., chamber gas spring 110 in FIGS. 3, 5A, and 5B, orcombined gas spring 130 in FIGS. 4, 6A, and 6B) is illustrated by theuppermost curve 140. The middle curve 145 represents the work carriedout by displacing a given volume of gas at a constant pressure. Thelowermost curve 150 represents the work supplied by the correctionforce. A low pressure chamber (e.g. low pressure chamber 70 in FIGS.3-5B) may be used to generate the required force and the related work.

FIG. 8 illustrates a graph of an example of the desired relationshipbetween the movement of the moveable structure 56 (x-axis) and the lowpressure piston 75 (y-axis) as a function of displacement. Thedisplacement of the low pressure piston 75 may be represented as anon-linear function of the moveable structure 56 displacement. Thenon-linear function may be implemented by using a non-linear linkageassembly 85, where the gear-versus-displacement function may beconfigured so that the desired relationship in displacement between thelow pressure piston 75 and the moveable structure 56 is obtained.

FIG. 9 illustrates an example technique for acquiring geophysical datathat may be used with embodiments of the present techniques. In theillustrated embodiment, a survey vessel 155 moves along the surface of abody of water 160, such as a lake or ocean. The survey vessel 155 mayinclude thereon equipment, shown generally at 165 and collectivelyreferred to herein as a “recording system.” The recording system 165 mayinclude devices (none shown separately) for detecting and making a timeindexed record of signals generated by each of seismic sensors 170(explained further below) and for actuating a marine vibrator 45 atselected times. The recording system 165 may also include devices (noneshown separately) for determining the geodetic position of the surveyvessel 155 and the various seismic sensors 170.

As illustrated, survey vessel 155 (or a different vessel) may tow one ormore marine vibrators 45 in body of water 160. In other embodiments,either in addition to or in place of the towed marine vibrators 45, oneor more marine vibrators 45 may be disposed at relatively fixedpositions in body of water 160, for example, attached to an anchor,fixed platform, anchored buoy, etc. Source cable 175 may couple marinevibrator 45 to survey vessel 155. Marine vibrator 45 may be disposed inbody of water 160 at a depth ranging from 0 meters to about 300 meters,for example. While only a single marine vibrator 45 is shown in FIG. 8,it is contemplated that embodiments may include more than one marinevibrator 45 (or other type of sound source) towed by survey vessel 155or a different vessel. In some embodiments, one or more arrays of marinevibrators 45 may be used. At selected times, marine vibrator 45 may betriggered, for example, by recording system 165, to generate acousticenergy. Survey vessel 155 (or a different vessel) may further tow atleast one sensor streamer 180 to detect the acoustic energy thatoriginated from marine vibrator 45 after it has interacted, for example,with rock formations 185 below water bottom 190. As illustrated, bothmarine vibrator 45 and sensor streamer 180 may be towed above waterbottom 190. Sensor streamer 180 may contain seismic sensors 170 thereonat spaced apart locations. In some embodiments, more than one sensorstreamer 180 may be towed by survey vessel 155, which may be spacedapart laterally, vertically, or both laterally and vertically. While notshown, some marine seismic surveys locate the seismic sensors 170 onocean bottom cables or nodes in addition to, or instead of, a sensorstreamer 180. Seismic sensors 170 may be any type of seismic sensorsknown in the art, including hydrophones, geophones, particle velocitysensors, particle displacement sensors, particle acceleration sensors,or pressure gradient sensors, for example. By way of example, seismicsensors 170 may generate response signals, such as electrical or opticalsignals, in response to detected acoustic energy. Signals generated byseismic sensors 170 may be communicated to recording system 165. Thedetected energy may be used to infer certain properties of thesubsurface rock, such as structure, mineral composition and fluidcontent, thereby providing information useful in the recovery ofhydrocarbons.

The foregoing figures and discussion are not intended to include allfeatures of the present techniques to accommodate a buyer or seller, orto describe the system, nor is such figures and discussion limiting butexemplary and in the spirit of the present techniques.

What is claimed is:
 1. A marine vibrator comprising: a containmenthousing, where the containment housing defines at least a portion of amarine vibrator internal volume having a marine vibrator internal gaspressure; a sound radiating surface; and a compliance chamber, whereinthe compliance chamber comprises: a compliance chamber housing, whereinthe compliance chamber housing defines at least a portion of acompliance chamber internal volume having a chamber gas spring; anon-linear linkage assembly; and a low pressure chamber, wherein the lowpressure chamber comprises: a low pressure piston coupled to thenon-linear linkage assembly, and a low pressure chamber housing, whereinthe low pressure chamber housing defines at least a portion of a lowpressure chamber internal volume having a low pressure chamber internalgas pressure, wherein a difference in the chamber gas spring and the lowpressure chamber internal gas pressure produces a pressure differentialacross the low pressure piston, wherein the low pressure piston isconfigured to move in response to the pressure differential across thelow pressure piston to change a resonance frequency of the marinevibrator.
 2. The marine vibrator of claim 1, wherein the non-linearlinkage assembly is coupled to the sound radiating surface.
 3. Themarine vibrator of claim 2, wherein movement of the low pressure pistongenerates a force on the sound radiating surface.
 4. The marine vibratorof claim 3, wherein the force generated by the low pressure piston onthe sound radiating surface mitigates at least a portion of the forcesexerted on the sound radiating surface by the marine vibrator internalgas pressure and the chamber gas spring.
 5. The marine vibrator of claim1, further comprising a moveable structure that at least partiallyseparates the marine vibrator internal volume from the compliancechamber internal volume.
 6. The marine vibrator of claim 5, wherein thenon-linear linkage assembly is coupled to the moveable structure.
 7. Themarine vibrator of claim 5, wherein the moveable structure comprises acompliance chamber piston.
 8. The marine vibrator of claim 5, whereinmovement of the low pressure piston generates a force on the moveablestructure.
 9. The marine vibrator of claim 8, wherein the forcegenerated by the low pressure piston on the moveable structure mitigatesat least a portion of a force exerted on the moveable structure by thechamber gas spring.
 10. The marine vibrator of claim 1, wherein thenon-linear linkage assembly comprises a camshaft and a low pressurechamber belt, wherein the low pressure chamber belt couples the camshaftto the low pressure piston.
 11. The marine vibrator of claim 1, whereinthe non-linear linkage assembly comprises ball bearings coupled to ribs.12. The marine vibrator of claim 1, wherein the compliance chamber isdisposed on the exterior of the containment housing.
 13. The marinevibrator of claim 1, wherein the marine vibrator comprises aflextensional shell-type marine vibrator, a piston plate marinevibrator, a hydraulically powered vibrator, an electro-mechanicalvibrator, an electrical marine vibrator, or a vibrator employingelectrostrictive (e.g., piezoelectric) or magnetostrictive material. 14.A method comprising: disposing a marine vibrator in a body of water inconjunction with a geophysical survey, wherein the marine vibratorcomprises: a containment housing, where the containment housing definesat least a portion of a marine vibrator internal volume having a marinevibrator internal gas pressure; a sound radiating surface; and acompliance chamber, wherein the compliance chamber comprises: acompliance chamber housing, wherein the compliance chamber housingdefines at least a portion of a compliance chamber internal volumehaving a chamber gas spring; a non-linear linkage assembly; and a lowpressure chamber, wherein the low pressure chamber comprises: a lowpressure piston coupled to the non-linear linkage assembly, and a lowpressure chamber housing, wherein the low pressure chamber housingdefines at least a portion of a low pressure chamber internal volumehaving a low pressure chamber internal gas pressure; triggering themarine vibrator to cause the sound radiating surface in the marinevibrator to move back and forth, the triggering resulting in adisplacement of a portion of the marine vibrator internal volume; andmoving the low pressure piston in response to the displacement of theportion of the marine vibrator internal volume to adjust a resonancefrequency of the marine vibrator.
 15. The method of claim 14, wherein aportion of the marine vibrator internal volume is displaced by movementof a moveable structure that separates the marine vibrator internalvolume from the compliance chamber internal volume.
 16. The method ofclaim 15, wherein movement of the low pressure piston generates a forceon the moveable structure.
 17. The method of claim 16, wherein the forcegenerated by the low pressure piston on the moveable structure mitigatesat least a portion of a force exerted on the moveable structure by thechamber gas spring.
 18. The method of claim 15, wherein movement of thelow pressure piston generates a force on the sound radiating surface.19. The method of claim 18, wherein the force generated by the lowpressure piston on the sound radiating surface mitigates at least aportion of a force exerted on the sound radiating surface by the marinevibrator internal gas pressure and the chamber gas spring.
 20. A methodcomprising: disposing a marine vibrator comprising a marine vibratorinternal gas pressure and a low pressure piston in a body of water at afirst depth, wherein the marine vibrator has a first resonance frequencyat the first depth; subsequently disposing the marine vibrator in thebody of water at a second depth, wherein the second depth is greaterthan the first depth, and wherein the marine vibrator has a secondresonance frequency at the second depth; and allowing marine vibratorinternal gas pressure to act on the low pressure piston such that thefirst resonance frequency differs from the second resonance frequency byno more than 25%.
 21. The method of claim 20, wherein the firstresonance frequency corresponds to a first power output and wherein thesecond resonance frequency corresponds to a second power output.
 22. Themethod of claim 20, wherein the first resonance frequency corresponds toa resonance frequency in the range of about 1 Hz to about 10 Hz andwherein the second resonance frequency corresponds to a resonancefrequency in the range of about 1 Hz to about 10 Hz.